Veteran broadcaster Paul Gambaccini said it had to be played, because the charts are "the news in a musical sense" and that no explanation should be needed as to why the song was charting.

But Tory MP John Whittingdale, Thatcher's former political secretary and chairman of the Commons Culture, Media and Sport committee, said it could present a "difficult" dilemma for the BBC.

Whittingdale told The Huffington Post UK: "I very much hope the issue will not arise, in that I would be very saddened if a song which will be being promoted on the basis of celebrating the death of Margaret Thatcher should achieve success that would be sufficient to put it into the charts.

"I think it would be difficult if that were the case, but I hope we're talking about an academic issue, not an actual one."

But another Tory MP, Rob Wilson, said Thatcher would not have wanted to censor the "nasty idiots" behind the campaign.

Gambaccini, who presented the US chart on BBC Radio 1 for 18 years, said: "There is no reason not to play it.

"The whole basis of the Sunday chart show is that it is the pop music equivalent of the news. You don't have to introduce every song with enthusiasm, you just play them."

There have been suggestions that the presenter could explain to younger listeners why the song was being played - but Gambaccini said this would be "precedent-setting."

"I am sure every 13-year-old in the country is aware that there's an internet campaign - they are on Facebook every day."

Record label-founder and music journalist Andy Ross said BBC bosses would be having "sleepless nights."

"This is a classic rock-and-a-hard-place situation, one which the producers at the beeb have - in a King Canute stance - chosen to defer until this Sunday, when they are having a summit."

He added: "I think it's enough to announce the track on the chart run-down, but is it worth the grief of actually playing it?

"I think the majority of other music stations won't mention it at all, but in the case of a public-funded entity such as the BBC, they should play it on the chart rundown."

A BBC Radio 1 spokesman said: "The Official Chart Show on Sunday is a historical and factual account of what the British public has been buying and we will make a decision about playing it when the final chart positions are clear.”

Margaret Thatcher Life In Pictures

Margaret Thatcher Life In Pictures

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Margaret Thatcher - General Election

Prime Minister Margaret Thatcher leaving 10 Downing Street after the Conservative Party won a convincing majority in the General Election.